50 www.racecar-engineering.com OCTOBER 2021
I remember doing a few laps of a track with a race driver instructor who showed me something: ‘Look, I can make the car understeer or oversteer,
it’s just about where in the corner entry I start to turn the steering wheel, and by how much.’ The demonstration was convincing, but not surprising. After all, without being too metaphysical, so many things in our life are decided by education and parenting, those early ‘inputs’. Why should vehicle dynamics be any different?
If it is true that a big part of car’s performance is defined by the reaction to the driver’s steering (and if required, braking) inputs at the corner entry, then we must carefully understand transient load transfers in the first metres of a corner.
Cutting corners In last month’s article (V31N9) we showed the decomposition of the load transfer on one axle in a geometric load transfer (depending on the roll centre altitude, and passing from one tyre to another via the suspension linkages) and an elastic load transfer (that is a function of the vertical distance between suspended mass c.g and the roll centre) that also passes from one tyre to the other through the springs, anti-roll bars and dampers, as shown in Figure 1.
With the lateral acceleration starting at 0.50 seconds, if we zoom in (Figure 2), 0.05 seconds later (0.05 seconds at 180km/h corresponds to 2.5m), we have about 65 per cent of the suspended mass load transfer that is geometric and about 35 per cent that is elastic, most of it (32 per cent) controlled by the dampers. After 0.10 seconds (five metres at 180km/h) 52.5 per cent of the suspended mass load transfer is geometric and 47.5 per cent is elastic, most of it (41.2 per cent) being, again, controlled by the dampers.
Before we draw some conclusions here, let us look at similar graphs with Figures 3 and 4. In Figure 3, with a roll centre below the ground, we can see that the geometric load transfer is negative, with a bigger elastic load transfer (peak at about 750N compared to 500N with a roll centre 75mm above the ground as seen in Figure 1).
If we zoom in (Figure 4), at 0.55 seconds we have about 52 per cent of the suspended
Entry requirements How load transfer plays out at the start of a corner and why it’s vital to understand exactly what a car‘s doing during these first few metres
BY CLAUDE ROUELLE
TECHNOLOGY – SLIP ANGLE
Put simply, at the entry of a left-hand corner the rear-right negative camber and toe-in are the back end of the car’s friends
Figure 1: Roll centre 75mm above ground – lateral acceleration and load transfer components
Figure 2: Roll centre 75mm above ground – percentage load transfer
Figure 1: The diagram above shows decomposition in a simplified open loop simulation with a lateral acceleration input of the geometric load transfer (which is shown with the red trace) and the different parts of the suspended mass elastic load transfers due to: springs (green), anti-roll bar (blue) and the dampers (purple), versus time with a fixed roll centre 75mm above the ground. Note that the non-suspended mass load transfer is not represented here
Figure 2: At the beginning of the corner (0.55 seconds) most of the suspended mass load transfer is geometric (65.3 per cent) and controlled by the dampers (32 per cent). After 0.10 seconds these percentages become 52.5 per cent and 41.2 per cent
Geometric WT Elastic (springs) FL Elastic (ARB) FL Elastic (dampers) FL Lateral acceleration
FL spring load FL ARB load FL damper load FL geometric load FL elastic load
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mass load transfer that is geometric and about 48 per cent elastic, most of it (about 44 per cent) controlled by the dampers. After 0.10 seconds (five metres at 180km/h) about 37 per cent of the suspended mass load transfer is geometric (red) and about 63 per cent is elastic (blue), most of it (about 54 per cent) being, again, controlled by the dampers.
What is the main conclusion then? If it is true that the first metres of a corner determines most of the car behaviour for the rest of it and, if because of a driver’s comments, you want to change the car handing at the very first part of the corner entrance, whether you want to increase or decrease the load transfer (and we will discuss this in the next paragraphs), it seems that the kinematics and the dampers are the first things you want to play with.
High tail Another thing I want to look at here is the often asked question: why does the rear roll centre need to be higher than the front? First, a quick reminder of the sequence of the force occurrence of the tyres in a corner is shown in Figure 5. From 5a to 5b the driver turns the steering wheel and creates a LF and RF steering angle. Things are not necessarily that immediate, depending on the steering system compliance, but that’s another story.
Due to the tyre’s relaxation length, it takes a few hundredths of second for the front tyre centripetal lateral forces to build as is seen in 5c; action = reaction; the sum of front tyres’ centripetal lateral force creates a centrifugal force acting on the car centre of gravity (F = Ma). You can do the sum of the moments around any point you want, and a yaw moment will be created. Depending on the yaw inertia you will create a yaw acceleration. A high yaw inertia will result in a low yaw acceleration and vice versa.
Now, in 5d the rear end of the car is moving sideways, rear tyre slip angles are created, and rear tyre lateral centripetal forces are created too. That will go on like this until the corner apex region (5e), where the sum of the front tyres’ lateral forces multiplied by the distance between the front axle and the c.g (distance a) will be equal to the sum of the rear tyres’ lateral forces multiplied by the distance between the c.g and the rear axle (distance b) and the yaw moment will be zero. Note that in this simplified explanation, we only consider four out of the twelve causes of the yaw moment, the four tyres’ lateral forces, Fy, and we ignore the four tyres’ longitudinal lateral forces, Fx, and self-alignments, Mz.
Importantly, no matter what, the rear tyres’ forces will always start later than the fronts. In some cases, we will want the rear tyres’ forces to ‘catch up’ with the fronts quicker. And that has something to do with the geometric load transfer, as we will soon see.
Figure 4: Roll centre 75mm below ground – percentage load transfer
Figure 5: Tyre forces sequence in a corner
Figure 3: Roll centre 75mm below ground – lateral acceleration and load transfer components
Figure 3: Decomposition of the geometric load transfer (red) and the different parts of the suspended mass elastic load transfers due to: springs (green), ARB (blue) and dampers (purple) versus time with a fixed roll centre 75mm below the ground and a simplified open loop lateral acceleration input (brown). The non-suspended mass load transfer is not represented here
Figure 4: At the beginning of the corner (0.55 seconds) most of the suspended mass load transfer is geometric (52.1 per cent) and controlled by the dampers (44.3 per cent). After 0.10 seconds these percentages become 36.9 per cent and 53.9 per cent
Figure 5. Evolution of the tyre slip angle, lateral forces, and the car yaw moment. Note that in this simplified explanation only the lateral forces on the four tyres are considered. The longitudinal forces and self-alignment moments are ignored
FL spring load FL ARB load FL damper load FL geometric load FL elastic load
Geometric WT Elastic (springs) FL Elastic (ARB) FL Elastic (dampers) FL Lateral acceleration
b. front wheel steering
c. front wheel slip angle, front lateral grip, lateral acceleration
e. rear slip angles, rear lateral grip, more lateral acceleration, more yaw velocity but less yaw moment
a. straight
52 www.racecar-engineering.com OCTOBER 2021
Now, let us have a look at a specific corner, a left-hander. In Figure 6 you can find the steering, speed, lateral and longitudinal acceleration inputs and speed input.
Knowing all the necessary car design and set-up information, the five essential parts of the data that are steering, speed, lateral and longitudinal accelerations (and vertical acceleration if the track has slopes and banking which is not the case here), and using the reverse engineering Track Replay from OptimumDynamics software, we can find the slip angles, slip ratios, vertical load, cambers forces and moments on each tyre.
Lateral thinking Let us now draw attention to the lateral forces at the beginning of the corner, shown in Figure 7. Ultimately all the lateral forces on the tyres will end up positive as we can see at the apex. The interesting part comes from the analysis of the lateral forces at the corner entry. If you revisit Figure 6 you can see that the lateral acceleration and steering only start at about 30 metres. Before that we only have braking. The lateral force on the LF (red) is positive before we even enter that left-hand corner. That is due to the front toe-out that is ‘preloading’ the LF tyre with a ‘good’ slip angle before we even need that lateral force. The side load due to the LF negative camber is not helping (that force pushes the car towards the corner outside) but, as the force generated by 0.1-degree of slip angle is usually much bigger than the one created by 0.1-degree of camber, the negative contribution of the LF negative camber is small compared to the positive effect of the LF toe-out.
On the RF (green), the toe-out is a ‘bad’ slip angle that generates a tyre lateral force that pushes the car towards the outside of the corner and its ‘good’ effect is smaller than the ‘bad’ effect of the negative RF camber thrust.
The lateral force on the RR (orange) is positive before we even enter the corner. That is due to the rear negative camber and the rear toe ‘preloading’ the RR tyre before we even need that lateral force. Put simply, at the entry of a left-hand corner the RR negative camber and toe-in are the rear end of the car’s friends. On the other hand, on the LR tyre (blue) the negative camber and toe-in (a ‘bad’ slip angle) are creating LR tyre lateral forces pushing the car towards the outside.
If you look carefully, you can see that from 30 metres (the beginning of the steering and lateral acceleration) until about 80 metres, the RF is not helping. The force is still negative. On the contrary, it helps the car to be pushed to the outside the corner. It’s the same for the LR until about 90 metres. On the RR, though, the lateral force is always pointing in the right direction (towards the corner inside).
If you want to increase the rear grip at a left-hand corner entry, then, or you want
Slip Angle is a summary of Claude Rouelle’s OptimumG seminars.
Public, on site, and online OptimumG seminars are held worldwide throughout the year. The Advanced Vehicle Dynamics and the Data Driven Performance Engineering seminars present several theories and best practices that can be used by engineers when making decisions on how to improve vehicle performance. OptimumG engineers can also be found around the world working as consultants for top level teams.
CONTACT Claude Rouelle Phone: + 1 303 752 1562 Enquiries: engineering@optimumg.com Website: www.optimumg.com
TECHNOLOGY – SLIP ANGLE
Figure 7: Dynamic lateral force
the rear grip to occur quicker, you need to capitalise on your friend (the RR) and also disinvest on your enemy (the LR). And how do you do that? By increasing the rear load transfer. And then how do you do that? By increasing the rear roll centre altitude because at the corner entry the biggest component of the load transfer is geometric.
Usually load transfer has a negative consequence on the car grip because, put simply, you lose more on the inside than you gain in the outside. But that is not always the case, as it depends on what the initial conditions of slip angle and camber are.
Here’s a practical application. The driver complains about turn-in oversteer, but is happy with the car for the rest of the corner. Whenever possible raise the rear roll centre to create more and/or quicker load transfer, to temporarily increase the rear grip where needed, and soften the rear ARB to get the same ‘magic number’ (total lateral load transfer distribution) at the apex.
Figure 6: Dynamic corner entry to exit – inputs
Figure 6. The steering wheel, lateral and longitudinal accelerations and speed inputs in a medium speed left-hand corner
Figure 7. Tyre lateral forces evolution in a corner based on the inputs shown in Figure 6, using the Track Replay function of OptimumDynamics and the acquired data of speed, steering, lateral and longitudinal accelerations. Note that the RF (shown in green) and LR (blue) remain negative for quite a way in to the corner entry
Steering wheel angle Lateral acceleration
Longitudinal acceleration Longitudinal speed